A new sixth-order algorithm for general second order ordinary differential equations

An important factor among others that should be considered in developing a numerical integrator for the solution of ordinary differential equations is the prudent management of computer time, which depends essentially on the number of functions to be evaluated per iteration. Recognising the importance of this factor, this article therefore proposes a class of four-step methods each with three functions evaluation per iteration. The procedure which yields a system of equations for stepnumber k ≥ 4 is based on collocation of the differential system at selected grid points which ensures the symmetry of the methods. The methods are compared for accuracy and computer time with an existing four-step method containing five functions evaluation per iteration (see Awoyemi, 1999a). Three other Predictors are similarly proposed for use in the main method.